On the minimum-norm least squares solution of the complex generalized coupled sylvester matrix equations

被引：3

作者：

Huang B. ^{[1
,2
]}

Ma C. ^{[1
]}

机构：

[1] School of Mathematics and Statistics & FJKLMAA, Fujian Normal University, Fuzhou

[2] School of Mathematical Sciences, South China Normal University, Guangzhou

来源：

Journal of the Franklin Institute | 2023年 / 360卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Algorithm for solving - Complex matrixes - Finite termination - Generalized coupled sylvester matrix equations - Initial matrixes - Iterative algorithm - Linear operators - Minimum norm least squares solutions - Minimum norm solutions - Real matrices;

D O I：

10.1016/j.jfranklin.2022.11.003

中图分类号：

学科分类号：

摘要：

By means of the real linear operator, we establish an iterative algorithm for solving a class of complex generalized coupled Sylvester matrix equations. The finite termination of the proposed algorithm is proved. By representing a complex matrix as a larger real matrix, we present a new method to prove that the minimum-norm solution or minimum-norm least squares solution of the complex generalized coupled Sylvester matrix equations can be obtained by an appropriate selection for the initial matrices, which has not been found in the existing work. Numerical experiments on some randomly generated data and practical image restoration problem show that the proposed algorithm is feasible and effective. © 2022 The Franklin Institute

引用

页码：3330 / 3363

页数：33

共 47 条

[11]

Xu L., Ding F., Zhu Q., Separable synchronous multi-innovation gradient-based iterative signal modeling from online measurements, IEEE Trans. Instrum. Meas., 71, (2022)

[12]

Xu L., Separable multi-innovation Newton iterative modeling algorithm for multi-frequency signals based on the sliding measurement window, Circ. Syst. Signal Pr., 41, pp. 1-26, (2022)

[13]

Zhang X., Ding F., Optimal adaptive filtering algorithm by using the fractional-order derivative, IEEE Signal Proc. Let., 29, pp. 399-403, (2022)

[14]

Zhou Y.H., Zhang X., Ding F., Partially-coupled nonlinear parameter optimization algorithm for a class of multivariate hybrid models, Appl. Math. Comput., 414, (2022)

[15]

Wu A.G., Fu Y.M., Duan G.R., On solutions of matrix equations V−AVF=BW and V−AV¯F=BW, Math. Comput. Model., 47, pp. 1181-1197, (2008)

[16]

Liao A.P., Bai Z.Z., Lei Y., Best approximate solution of matrix equation AXB+CYD=E, SIAM J. Matrix Anal. Appl., 27, pp. 675-688, (2005)

[17]

Ding F., Liu P.X., Ding J., Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Appl. Math. Comput., 197, pp. 41-50, (2008)

[18]

Ding J., Liu Y., Ding F., Iterative solutions to matrix equations of the form AiXBi=Fi, Comput. Math. Appl., 59, pp. 3500-3507, (2010)

[19]

Ding F., Zhang H.M., Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems, IET Control Theory A., 8, pp. 1588-1595, (2014)

[20]

Heyouni M., Saberi-Movahed F., Tajaddini A., On global Hessenberg based methods for solving Sylvester matrix equations, Comput. Math. Appl., 77, pp. 77-92, (2019)

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